Question

$\sqrt{96} + \sqrt{6} =
\sqrt{8} \cdot \sqrt{3} =
2\sqrt{6}
\sqrt{102}
5\sqrt{6}
4\sqrt{6}$

Explanation:

First, solve \(\boldsymbol{\sqrt{96} + \sqrt{6}}\)

Step1: Simplify \(\sqrt{96}\)

Factor 96 to find perfect square factors: \(96 = 16\times6\), so \(\sqrt{96}=\sqrt{16\times6}=\sqrt{16}\times\sqrt{6}=4\sqrt{6}\)

Step2: Add \(\sqrt{6}\)

Now, \(\sqrt{96}+\sqrt{6}=4\sqrt{6}+\sqrt{6}\). Combine like terms: \((4 + 1)\sqrt{6}=5\sqrt{6}\)

Next, solve \(\boldsymbol{\sqrt{8}\cdot\sqrt{3}}\)

Step1: Use the property \(\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\)

So, \(\sqrt{8}\cdot\sqrt{3}=\sqrt{8\times3}=\sqrt{24}\)

Step2: Simplify \(\sqrt{24}\)

Factor 24: \(24 = 4\times6\), so \(\sqrt{24}=\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}=2\sqrt{6}\)

For \(\boldsymbol{\sqrt{96} + \sqrt{6}}\), the answer is \(5\sqrt{6}\).
For \(\boldsymbol{\sqrt{8}\cdot\sqrt{3}}\), the answer is \(2\sqrt{6}\).

Answer:

Step1: Use the property \(\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\)

So, \(\sqrt{8}\cdot\sqrt{3}=\sqrt{8\times3}=\sqrt{24}\)

Step2: Simplify \(\sqrt{24}\)

Factor 24: \(24 = 4\times6\), so \(\sqrt{24}=\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}=2\sqrt{6}\)

For \(\boldsymbol{\sqrt{96} + \sqrt{6}}\), the answer is \(5\sqrt{6}\).
For \(\boldsymbol{\sqrt{8}\cdot\sqrt{3}}\), the answer is \(2\sqrt{6}\).